In the light of descriptive geometry and notions in set theory, this paper redefines the basic elements in space such as curve and surface and so on, presents some fundamental notions with respect to the point cover based on the High-Dimension Space(HDS) point covering theory, finally takes points from mapping part of speech signals to HDS, so as to analyze distribution information of these speech points in HDS, and various geometric covering objects for speech points and their relationship. Besides, this paper also proposes a new algorithm for speaker independent continuous digit speech recognition based on the HDS point dynamic searching theory without endpoints detection and segmentation. First from the different digit syllables in real continuous digit speech, we establish the covering area in feature space for continuous speech. During recognition, we make use of the point covering dynamic searching theory in HDS to do recognition, and then get the satisfying recognized results. At last, compared to HMM-based method, from the development trend of the comparing results, as sample amount increasing, the difference of recognition rate between two methods will decrease slowly, while sample amount approaching to be very large, two recognition rates all close to 100% little by little. As seen from the results, the recognition rate of HDS point covering method is higher than that of in HMM-based method, because, the point covering describes the morphological distribution for speech in HDS, whereas HMM-based method is only a probability distribution, whose accuracy is certainly inferior to point covering.
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